Problem: What is the value of the following logarithm? $\log_{256} 4$
Answer: If $b^y = x$ , then $\log_{b} x = y$ Notice that $4$ is the fourth root of $256$ That is, $\sqrt[4]{256} = 256^{1/4} = 4$ Thus, $\log_{256} 4 = \dfrac{1}{4}$.